The Barometer Story

by Alexander Calandra - an article from Current Science, Teacher's Edition,
1964.

Some time ago, I received a call from a colleague who asked if I would be
the referee on the grading of an examination question. It seemed that he was
about to give a student a zero for his answer to a physics question, while the
student claimed he should receive a perfect score and would do so if the
system were not set up against the student. The instructor and the student
agreed to submit this to an impartial arbiter, and I was selected.

The Barometer Problem

I went to my colleague's office and read the examination question, which
was, "Show how it is possible to determine the height of a tall building with
the aid of a barometer."

The student's answer was, "Take the barometer to the top of the building,
attach a long rope to it, lower the barometer to the street, and then bring it
up, measuring the length of the rope. The length of the rope is the height of
the building."

Now, this is a very interesting answer, but should the student get credit
for it? I pointed out that the student really had a strong case for full
credit, since he had answered the question completely and correctly. On the
other hand, if full credit were given, it could well contribute to a high
grade for the student in his physics course. A high grade is supposed to
certify that the student knows some physics, but the answer to the question
did not confirm this. With this in mind, I suggested that the student have
another try at answering the question. I was not surprised that my colleague
agreed to this, but I was surprised that the student did.

Acting in terms of the agreement, I gave the student six minutes to answer
the question, with the warning that the answer should show some knowledge of
physics. At the end of five minutes, he had not written anything. I asked if
he wished to give up, since I had another class to take care of, but he said
no, he was not giving up. He had many answers to this problem; he was just
thinking of the best one. I excused myself for interrupting him, and asked him
to please go on. In the next minute, he dashed off his answer, which was:

"Take the barometer to the top of the building and lean over the edge of
the roof. Drop the barometer, timing its fall with a stopwatch. Then, using
the formula S= 1/2 at^2, calculate the height of the building."

At this point, I asked my colleague if he would give up. He conceded and I
gave the student almost full credit. In leaving my colleague's office, I
recalled that the student had said he had other answers to the problem, so I
asked him what they were.

"Oh, yes," said the student. "There are many ways of getting the height of
a tall building with the aid of a barometer. For example, you could take the
barometer out on a sunny day and measure the height of the barometer, the
length of its shadow, and the length of the shadow of the building, and by the
use of simple proportion, determine the height of the building."

"Fine," I said. "And the others?"

"Yes," said the student. "There is a very basic measurement method that you
will like. In this method, you take the barometer and begin to walk up the
stairs. As you climb the stairs, you mark off the length of the barometer
along the wall. You then count the number of marks, and this will give you the
height of the building in barometer units. A very direct method.

"Of course, if you want a more sophisticated method, you can tie the
barometer to the end of a string, swing it as a pendulum, and determine the
value of 'g' at the street level and at the top of the building. From the
difference between the two values of 'g', the height of the building can, in
principle, be calculated."

Finally, he concluded, "If you don't limit me to physics solutions to this
problem, there are many other answers, such as taking the barometer to the
basement and knocking on the superintendent's door. When the superintendent
answers, you speak to him as follows: 'Dear Mr. Superintendent, here I have a
very fine barometer. If you will tell me the height of this building, I will
give you this barometer.'"

At this point, I asked the student if he really didn't know the answer to
the problem. He admitted that he did, but that he was so fed up with college
instructors trying to teach him how to think and to use critical thinking,
instead of showing him the structure of the subject matter, that he decided to
take off on what he regarded mostly as a sham.